My opinion is that the Shure 565 should work just fine for you. If it's still functioning, there's no reason to switch horses unless there is something particular you don't like about the sound.

I would fully explore the options you have available with the UX1/Shure 565 combo you currently have in hand.

On this page at the Line6 site, it talks about all the different modeled microphone pre-amps that are available - that's some cool stuff to play with right there.

http://line6.com/toneportux1/vocals.html

This is what you currently own from a mic pre-amp modeling standpoint.

If you can't get a decent sound using the Shure with the UX1 and tweaking one of these mic pre-amp setups, the AKG isn't going to help either.

-Scott